We report on a Stokesian Dynamics simulation study of monolayers of spheric
al colloidal particles diffusing in the midplane between two parallel walls
. The method accounts for many-body hydrodynamic interactions (HI) between
particles and particles and walls. Two cases are studied: hard spheres betw
een neutral walls and charged particles interacting by a Yukawa-type potent
ial. Various properties are calculated: mean-squared displacement, self-dif
fusion coefficient, von Hove functions and hydrodynamic functions. The impo
rtance of HT is assessed by treating particle-particle and particle-wall HI
separately. Striking features are discussed like the hydrodynamic enhancem
ent of self-diffusion for strongly charged particles and the unbounded incr
ease of the hydrodynamic function at small wave numbers.